damage mechanism and stress response of reinforced

Coupled Systems Mechanics, Vol. 8, No. 4 (2019) 315-338

DOI: https://doi.org/10.12989/csm.2019.8.4.315 315

Copyright © 2019 Techno-Press, Ltd. http://www.techno-press.org/?journal=csm&subpage=8 ISSN: 2234-2184 (Print), 2234-2192 (Online)

Damage mechanism and stress response of reinforced concrete slab under blast loading

K. Senthil*, A. Singhala and B. Shailjab

Department of Civil Engineering, Dr. B R Ambedkar National Institute of Technology Jalandhar, Jalandhar, Punjab 144011, India

(Received February 3, 2019, Revised May 15, 2019, Accepted June 4, 2019)

Abstract. The numerical investigations have been carried out on reinforced concrete slab against blast

loading to demonstrate the accuracy and effectiveness of the finite element based numerical models using

commercial package ABAQUS. The response of reinforced concrete slab have been studied against the

influence of weight of TNT, standoff distance, boundary conditions, influence of air blast and surface blast.

The results thus obtained from simulations were compared with the experiments available in literature. The

inelastic behavior of concrete and steel reinforcement bar has been incorporated through concrete damage

plasticity model and Johnson-cook models available in ABAQUS were presented. The predicted results

through numerical simulations of the present study were found in close agreement with the experimental

results. The damage mechanism and stress response of target were assessed based on the intensity of

deformations, impulse velocity, von-Mises stresses and damage index in concrete. The results indicate that

the standoff distance has great influence on the survivability of RC slab against blast loading. It is concluded

that the velocity of impulse wave was found to be decreased from 17 to 11 m/s when the mass of TNT is

reduced from 12 to 6 kg. It is observed that the maximum stress in the concrete was found to be in the range

of 15 to 20 N/mm2 and is almost constant for given charge weight. The slab with two short edge

discontinuous end condition was found better and it may be utilised in designing important structures. Also it

is observed that the deflection in slab by air blast was found decreased by 60% as compared to surface blast.

Keywords: reinforced concrete slab; damages; blast loading; mass of TNT; finite element analysis;

deformation

1. Introduction

In the past few decades, damage to a structure due to explosion has increased as a result of

increase in number and intensity of terrorist activities, manmade accident, and natural explosion

during earthquake, climatic changes etc. In order to design structures which are able to withstand,

it is necessary to first quantify the effects of such explosions. Typically, it is calculated from

various sources such as professional guides, experimental tests and analytical tools. Nowadays,

blast resistant design is becoming an important part of the design since the vulnerabilities due to

Corresponding author, Assistant Professor, E-mail: [email protected], [email protected] aPost Graduate Student, E-mail: [email protected] bAssistant Professor, E-mail: [email protected]

K. Senthil, A. Singhal and B. Shailja

widespread terrorist activities. Keeping this in mind, research communities all over the world are

seeking solutions for potential blasts, protecting building occupants and the structures. Ettouney et

al. (1996) presented design of commercial building subjected to blast loading. It is observed that

the design modifications and recommendations that improve ductility and structural response

during occurrence of blast load. Watson et al. (2005) carried out experiments and measured the

damages caused to reinforced concrete T beams and slabs by contact and close proximity

explosive charges using different areas of contact and angles of inclination for the explosives.

Experiments of blast on the prototype and model specimens were conducted and found in

agreement between the prototype and model response. Osteras et al. (2006) discussed qualitative

assessment of blast damage and collapse pattern of murrah Building bombing in 1995. The

destruction was mainly due to combination of direct blast effects that destroyed one column and

large portions of the second, third and perhaps portions of the fourth floor slab. It is concluded that

a complete three dimensional space frame that interconnects all load path provides stability. Ngo et

al., (2007) and Ngo and Mendis (2009) presents a comprehensive overview of the effects of

explosion on structures. An explanation of the nature of explosions and the mechanism of blast

waves in free air is given. Authors were introduced different methods to estimate blast loads and

structural response. King et al. (2009) discussed typical building retrofit strategies for load bearing

and non-load bearing structural members through strengthening, shielding, or controlling

hazardous debris. Shi et al. (2009) also conducted numerical investigations to investigate the bond-

slip effect on numerical analysis of blast-induced responses of a RC column. Wu et al. (2009)

presented study on blast resistance of normal reinforced concrete (NRC), ultra-high performance

fibre (UHPFC) and FRP-retrofitted concrete slab (RUHPFC). The results indicates that the plain

UHPFC slab had a similar blast resistance to the NRC slab and that the RUHPFC slab was

superior to both.

Wakchaure and Borole (2013) compared between long side and short side column and

percentage of stress of reinforced concrete column for long and short side is presented an analysis

is carried out using ANSYS. It was conclude that the critical impulse for the long column case

found to be significantly higher. Samir (2014) performed numerical simulations on reinforced

concrete columns subjected to various blast loads using the finite element software ABAQUAS.

The effects of transverse and longitudinal reinforcement ratios, charge weight and column aspect

ratio were the parameters considered. It was concluded that the residual displacement becomes

more significant after a certain charge weight. Yi et al. (2014) presented new approach (Hybrid

blast load method instead of pressure load or detonation simulation method) for the applications of

blast loads on bridge components. Hybrid blast load method uses realistic loads and able to

simulate both reflection and diffraction of blast loads using LS DYNA. It is concluded that the

proposed model is advantageous over pressure load model as it predicts more conservative results.

Burrel et al. (2015) present study on response of steel fiber-reinforced concrete (SFRC) column

subjected to blast loading. It is concluded that SFRC improves the blast performance of columns in

terms of maximum and residual displacements as well as damage tolerance and elimination of

secondary blast fragments. Liu et al. (2015) presented simplified blast load effects on the column

and bent beam of highway bridges using finite element model. Study shows that the above model

may reproduce many of the damage mechanism of typical highway bridge. It is observed that the

provision of transverse reinforcement improved the blast resistance of highway bridges.

Wijesundara and Clubley (2016) also investigates the effect of time-variant coupled uplift forces

and lateral blast pressures on the vulnerability of reinforced concrete columns when subjected to

internal explosions. Yao et al. (2016) conducted experimental and numerical investigation on

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concrete slabs against blast loading. The results shows that the deflection thickness ratio of RC

slab is inversely proportional to the scale distance and the reinforcement ratio. It is observed from

the results that reinforcement ratio has great influence on survivability of reinforced concrete slab

under blast loading. Zhang and Phillips (2016) presented performance and protection of base

isolated structures under blast loading. Supplemental control devices are proposed and it is

concluded that it gives satisfactory results. Sami (2017) presented numerical study on the uplift

response of reinforced concrete slabs subjected to internal explosions. It is concluded that the

ultimate capacity is governed by tensile membrane action and that most critical sections were slab

supports. In addition to that, many studies found on detailed experiments and finite element

analysis [Ibrahimbegovic (1990), Ibrahimbegovic and Wilson (1991)] using reinforced concrete

slab subjected to blast loading [Lu (2009), Xue et al. (2013), Dehghani (2018), Lotfi and Zahrai

(2018), Zhang et al. (2018), Senthil et al. (2018), Singhal et al. (2018)], however, there are

significant shortcomings which is derived from the previous studies.

Based on the detailed literature survey, it is observed that most studies focused on simple

experiments on simple slabs, column and bridge elements subjected to blast loading, however

numerical investigations on slabs against blast loading has been found to be limited. Also response

of the reinforced concrete slab subjected to blast loading under varying mass of TNT has not been

studied. None of the author performed simulations on reinforced concrete slab under air blast and

surface blast conditions. In the present study, the numerical investigations has been carried out on

reinforced concrete slab against blast loading through finite element method. The inelastic

behavior of concrete and steel reinforced bar has been incorporated through concrete damage

plasticity model and Johnson-cook model respectively and discussed in Section 2. The finite

element model have been carried out using commercial tool ABAQUS/CAE is discussed in

Section 3. The results obtained from simulations were compared with the experiments available in

literature, Li et al. (2016). The simulations are carried out against varying standoff distance, mass

of TNT, boundary conditions and type of blast and discussed in Section 4. The damage intensity

and stresses of reinforced concrete slab were studied in light of deflection, impulsive wave

velocity, von-Mises stresses, compression damage of concrete.

2. Constitutive modelling

The inelastic behavior of concrete has been incorporated through concrete damage plasticity

model and the model includes compressive and tensile behavior. The elastic and plastic behavior

of steel reinforcement bar has been incorporated using Johnson-cook model includes the effect of

state of stress, temperature and strain rate and discussed in this section.

2.1 Concrete damaged plasticity model for concrete

In finite element modelling, inelastic behaviour of concrete was defined by using concrete

damaged plasticity model (CDP) providing a general capability for modelling concrete and other

quasi-brittle materials. The plastic-damage model is a form of plasticity theory in which a plastic-

damage variable ‘K’ was defined which increases if plastic deformation takes place. Moreover, the

plastic-damage variable is limited to a maximum value and the attainment of this value at a point

of the solid represents total damage, which can be interpreted as the formation of a macroscopic

crack. The variable “K” is non-dimensional and its maximum value is unity. The concrete

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Table 1 Compressive damage variables for CDP model

Yield Stress (N/mm2) Inelastic Strain Damage Parameter (dc)

15.00 0 0

14.32 0.000475 0.045

14.07 0.000575 0.061

13.53 0.000775 0.097

13.25 0.000875 0.116

12.69 0.001075 0.153

12.13 0.001675 0.191

10.60 0.001875 0.293

10.14 0.002875 0.323

7.22 0.003575 0.351

Table 2 Tensile damage variables for CDP model

Yield Stress (N/mm2) Cracking Strain Damage Parameter (dt)

2.71 0 0

2.30 0.0004 0.211

2.20 0.0008 0.256

2.00 0.0009 0.312

1.91 0.002 0.384

Table 3 Material parameters of concrete, Jankowiak and Lodygowski (2005)

Description Notations Numerical value

Modulus of elasticity E (N/m2) 19365 x 106

Poisson's ratio ѵ 0.2

Density 𝜌 (kg/m3) 2400

Eccentricity e 0.1

Dilation angle Ψ (degree) 38

Bulk modulus k 0.667

fb0/fc0 Ratio - 1.16

damaged plasticity model is a continuum, plasticity-based, damage model for concrete. The model

assumes that the two main failure mechanisms are tensile cracking and compressive crushing of

the concrete material. The evolution of the yield surface is controlled by two hardening variables

which are linked to failure mechanisms under tension and compression loading, namely εcpl and εt

pl

are compressive and tensile equivalent plastic strains, respectively. The damage variables can take

values from zero to one, where zero represents the undamaged material and one represents total

loss of strength. The stress strain relations under uniaxial compression and tension loading are

given by the following equations where Eo is the initial (undamaged) elastic stiffness of the

material: σt = (1-dt)Eo(εt-εtpl) and σc = (1-dc)Eo(εc-εc

pl), where dt and dc are tension damage variable

and compression damage variable respectively, Senthil et al. (2017). The concrete damaged

plasticity model parameters such as (dt) tension and (dc) compression damage variables are shown

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Table 4 Material parameters for steel reinforcing bar, Iqbal et al. (2015)

Description Notations Numerical value

Modulus of elasticity E (N/mm2) 203000

Poisson’s ratio ʋ 0.33

Density 𝜌 (Kg/m3) 7850

Yield Stress constant A (N/mm2) 304.330

Strain hardening constant B (N/mm2)

n

422.007

0.345

Viscous effect C 0.0156

Thermal softening constant m 0.87

Reference strain rate ε̇0 .0001 s-1

Melting temperature 𝜃melt (K) 1800

Transition temperature 𝜃transition (K) 293

Fraction strain constant

D1

D2

D3

D4

D5

0.1152

1.0116

-1.7684

-0.05279

0.5262

in Tables 1 and 2. The compressive strength of concrete was considered 15 MPa and Poisson’s

ratio of the concrete was assumed equal to 0.20. The parameters for CDP model other than

damage variables are shown in Table 3.

2.2 Johnson-Cook model for reinforcement

The flow and fracture behavior of projectile and target material was predicted employing the

Johnson-Cook (1985) elasto-viscoplastic material model available in ABAQUS finite element

code. The material model is based on the von Mises yield criterion and associated flow rule. It

includes the effect of linear thermo-elasticity, yielding, plastic flow, isotropic strain hardening,

strain rate hardening, softening due to adiabatic heating and damage. The Johnson and Cook

(1985) extended the failure criterion proposed by Hancock and Mackenzie (1976) by incorporating

the effect of strain path, strain rate and temperature in the fracture strain expression, in addition to

stress triaxiality. The fracture criterion is based on the damage evolution wherein the damage of

the material is assumed to occur when the damage parameter, exceeds unity: The strain at failure is

assumed to be dependent on a non-dimensional plastic strain rate, a dimensionless pressure-

deviatoric stress ratio, (between the mean stress and the equivalent von-Mises stress) and the non-

dimensional temperature, defined earlier in the Johnson-Cook hardening model. When material

damage occurs, the stress-strain relationship no longer accurately represents the material behavior,

ABAQUS (2008). The use of stress-strain relationship beyond ultimate stress introduces a strong

mesh dependency based on strain localization i.e., the energy dissipated decreases with a decrease

in element size. Hillerborg’s fracture energy criterion has been employed in the present study to

reduce mesh dependency by considering stress-displacement response after the initiation of

damage. The section of the reinforcement is assigned Fe250 steel and the ultimate tensile strength

is 250 MPa is approximately equivalent to the ultimate tensile strength proposed by Iqbal et al.

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(2015) and the material properties of the steel reinforcing bar has been shown in Table 4.

3. Finite element modelling

The finite element model of the reinforced concrete slab was made using ABAQUS/CAE. The

length and width of slab was 2.0 and 0.8 m respectively exactly proposed by Li et al. (2016), see

Fig. 1 Schematic of reinforced concrete slab, Li et al. (2016)

(a) (b)

Fig. 2 Modelling of (a) reinforcement and (b) concrete

(a) (b)

Fig. 3 Picture showing (a) Experimental setup (Li et al. 2006) and (b) Simulation

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Fig. 4 Finite element modelling of (a) main reinforcement (b) stirrups (c) combination of main

reinforcement and stirrups and (d) concrete

Fig. 1. The thickness of slab was 120 mm and clear cover is 20 mm on both the side of slab. The

top and bottom steel reinforcement of main bar was 12 mm diameter placed at 95 mm center to

centre distance. The size of stirrup reinforcement in slab was considered as 10 mm diameter placed

at 196 mm centre to centre distance on shorter direction, see Fig. 1. The geometry of the concrete

and steel reinforcement was modelled as solid deformable body, Fig. 2(a)-2(b). The interaction

between concrete and steel was modelled using the tie constraint option available in

ABAQUS/CAE wherein the concrete was assumed as host region and the steel as embedded

region. The constitutive and fracture behavior of steel and concrete have been predicted using

Johnson-Cook and Concrete damaged plasticity model respectively available in ABAQUS. The

origin of blast considered against 1.5 m from the exterior top surface of slab and 8 kg mass of

TNT.

Fig. 3(a) showing the slab placed on a steel frame with the height of 600 mm above the ground,

(Li et al. 2016). The combined model of slab has been shown in Fig. 3(b) and the rotational and

translational motion of the slab was restricted to depict rigid supports at the ends. The blast load

was incorporated using interaction module available in ABAQUS. The surface blast load was

created using CONWEP definition and the surface blast was consigned with help of two reference

point (RP-1 and RP-2) which is assigned based on standoff distance from point of response. For

surface blast two reference points were created and in case of air blast loading, one reference point

was created. For instances, in case of Fig. 3(b), is on surface blast need two reference points to be

selected based on standoff distance from centre of slab. The detonator was hexogen (RDX) and the

parameters considered for blast load is exactly similar to Li et al. (2016). In the present study, the

response was measured from the location where maximum damage/deformation/stresses exists

otherwise it is chosen at middle of slab. The boundary conditions were defined as clamped at

shorter directions and it is proximity of the experiments clamped at its both ends with steel cleats

and bolts. This set-up is assumed as an idealized fixed end boundary which prevents slab from

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(a) (b)

Fig. 5 Deflection of slab function of (a) varying mesh size and (b) time

Fig. 6 Von-Mises stresses and deformation of slab against (a) 10 (b) 15 (c) 20 and (d) 30 mm mesh sizes

rebounding under severe blast loads. The possible explanation regarding design of tests has been

given in the manuscript however, a detailed schematic of geometry and the tests conditions were

given in Figs. 1 and 2 and Li et al. (2016).

The mathematical modelling/constitutive modelling in order to define the damage behaviour of

concrete and steel reinforcement has been elaborated in detail in (Iqbal et al. 2015 and Senthil et

al. 2017), however, the damage and the material parameters has been incorporated, please see

Tables 1-4. The typical finite element modelling of steel reinforcement and concrete of wall

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element has been shown in Fig. 4(a)-4(d). The concrete elements of all the components were

meshed using structured elements of 8 noded hexahedral linear brick element and steel

reinforcement was meshed with linear beam element. Linear shape functions were used by

elements and reduced integration was considered, i.e. per element one integration point. A linear

element of type T3D2 (three dimensional two noded truss element) reduced integration. A detailed

mesh sensitivity analysis has been carried out to understand the influence of mesh size. The size of

element was varied as 0.03 × 0.03 × 0.03 m, 0.02 × 0.02 × 0.02 m, 0.015 × 0.015 × 0.015 m and

0.01 × 0.01 × 0.01 m and corresponding total number of elements were 7236, 24000, 56392 and

192000 respectively.

The predicted deflection of slab was compared with the experimental results, see Fig. 5(a)

corresponding to varying mesh size. The predicted deflection at middle of the slab was 215, 190,

179 and 135 mm against 10, 15, 20 and 30 mm mesh size respectively, see Fig. 5(b), whereas the

measured deflection through experiment was 190 mm. It is observed that the deflection of slab

corresponding element size of 15 and 20 m was found in good agreement with the experimental

results. In addition to that the maximum deflection and Mises stresses in concrete as well as steel

reinforcement of varying mesh sizes were compared, see Fig. 6(a)-6(d). It is observed that the

Mises stresses in concrete was found to be 29, 22, 18.2 and 17.9 MPa against 10, 15, 20 and 30

mm mesh size respectively. The Mises stresses in steel reinforcement was found to be 377, 371,

358 and 342 MPa against 10, 15, 20 and 30 mm mesh size respectively. Therefore, it is concluded

that the mesh size of 20 mm for both reinforcement bar and concrete was found to be suitable for

further analysis considering the less computational time and cost. The mesh size of concrete as

well as reinforced bar was considered as 20 × 20 × 20 mm. The mesh size 20 mm was assigned,

giving a total number of 24000 and 2688 elements for the concrete and reinforced steel bar

respectively. The analysis was divided into 20 frames within a time frame of 0.08 second. A CPU

time typical simulation for blast event took around 41 hours and 20 minutes.

4. Comparison of experimental and numerical results

The simulations were carried out against 8 kg mass of TNT at a distance of 1.5 from the surface

of the slab. The concrete damaged plasticity model has been employed for predicting the material

behavior of the concrete, whereas the Johnson-Cook model has been used for predicting the

material behavior of steel reinforcement. The three dimensional finite element modelling of the

slab including steel reinforcement is discussed in Section 3. The simulated results thus obtained

have been compared with the experiments carried out by Li et al. (2016) and discussed in this

Section.

Fig. 7(a)-7(f) shows the deformed profile of experiments and predicted results in light of

displacement, compression damage, tension damage, Mises stress in concrete and steel. It is

observed that the maximum deflection obtained numerically is 185 mm, which is very close to the

maximum deflection of 190 mm measured throughout the experiment. The predicted deflections

are in close agreement to actual experimental results. However, the maximum difference between

the actual and predicted deflection was found to be 3%. The predicted concrete compression and

tension damage index were 0.336 and 0.385 found closely matching with the input of 0.351 and

0.38, respectively are shown in Table 1. The predicted von-Mises stresses in concrete was 18.2

MPa is almost equivalent to the compressive strength of concrete 15 MPa measured from the

experiments. The predicted equivalent von-Mises stresses in the reinforcement bar was 525 MPa

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Fig. 7 Deformed profile of (a) experiments and predicted results of (b) displacement (c) compression

damage (d) tension damage (e) Mises stress in concrete and (f) Mises stress in steel

Fig. 8 Pressure-Impulse waves against blast load by varying mass of TNT at a distance of 1.5 m

which is close to the true stress measured from the experiment, Iqbal et al. (2015). The actual and

predicted deformation of the slab as a result of failure has been compared and almost exact pattern

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of deformation has been predicted through numerical simulations. For further understanding, the

Pressure-Impulse waves were obtained against the blast load by varying mass of TNT at a distance

of 1.5 m using CONWEP commend available in ABAQUS is shown in Fig. 8. The maximum

impulsive pressure generated through simulation was 29, 25 and 24 MPa, against 6, 8 and 12 kg

mas of TNT, respectively.

5. Results and discussion

Three-dimensional finite element analysis has been carried out in order to study the response of

reinforced concrete slab against blast loading using ABAQUS/CAE. The simulations were carried

out against varying standoff distance, mass of TNT and different support condition. Also the

response of slab have been studied against surface blast as well as air blast loading. The response

of structural elements were observed in terms of deflection, impulsive velocity, von-Mises stresses

and compression damage therein were presented and discussed.

5.1 Effect of varying mass of TNT

The simulations were carried out against varying mass of TNT at constant standoff of distance,

i.e. 1.5 m. The response of 120 mm thick slab was studied against varying mass of TNT and the

mass considered as 6.0, 8.0 and 12 kg. The behaviour of reinforced concrete slab in terms of

deflection, impulse velocity, Mises stresses in concrete and steel bar and compression damage

against varying mass of TNT is shown in Figs. 9 and 10.

The displacement of slab against blast load of varying mass TNT originated at 1.5 m from the

surface is shown in Fig. 9(a-i)-(c-i). The unit of the displacement contours was “meter”. The

maximum deflection was found to be 307, 185 and 120 mm against 12, 6 and 8 kg mass TNT

respectively. It is observed that the deflection in the slab was found to be increased by 156% when

the mass of TNT increased from 6 to 12 kg. It is concluded that for every increase of 33.33%

weight of TNT, the deflection increases by 52% for a standoff distance of 1.5m. The maximum

deflection on slab was about 307 mm against mass of 12 kg TNT and it is found to be more

vulnerable. The deflection of slab against 12 kg mass was found increased to 39 and 60% as

compared to the deflection of slab by 6 and 8 kg mass TNT respectively. It is also clearly seen that

the deflection reaches its peak value within 0.02 seconds i.e., from the time of detonation, see Fig.

10(a).

The impulse velocity due to the blast due to varying mass of TNT has been shown in Fig. 9(a-

ii)-(c-ii). The unit of the velocity contours was “meter per second”. The maximum impulse

velocity 11, 13.2 and 17.9 m/s against 6, 8 and 12 kg mass TNT respectively. It is observed that

the impulsive velocity was found to increase with increase in mass of TNT. The impulse velocity

against 12 kg mass was found increased to 61 and 73% as compared to the velocity of 6 and 8 kg

mass TNT respectively. As it was clearly seen that velocity reaches its maximum within 0.02

seconds after which it drops to almost zero, see Fig. 10(b).

The compression damage index of reinforced concrete slab against blast load of varying mass

TNT is shown in Fig. 9(a-iii)-(c-iii). The compression damage contours described by unit less

factor. The maximum damage due to compression was found to be 0.336 for against all chosen

mass of TNT. The compression damage parameter was considered maximum of 0.351 in the

present study. It is observed that the compression damage in the slab was found to reach maximum

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Fig. 9 (i) Deflection of slab (ii) impulse velocity (iii) compression damage (iv) Mises stresses in concrete

and steel bar and against (a) 6 (b) 8 and (c) 12 kg mass TNT

(a) (b)

Fig. 10 Response in terms of (a) deflection and (b) impulse velocity function of time at varying mass of TNT

against 6 kg mass TNT. Also it was observed that the damage intensity was found increasing with

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increase of mass of TNT. From this observation, it is concluded that the slab was found to be more

vulnerable against 6 kg mass of TNT and the slab may be safe if the mass of TNT below 6 kg.

The von-Mises stresses in concrete against blast load of varying mass TNT is shown in Fig.

9(a-iv)-(c-iv). The unit of the von-Mises stress in the contours is “N/m2”. At 0.004 second time

step, the maximum von-Mises stress at the concrete was found to be 36, 39.8 and 30.4 MPa for 6,

8 and 12 kg mass TNT respectively. However, it is observed that the stress in concrete was found

to be almost 20 MPa after 0.004 second time step. The highest stress is at 0.004 second, it may be

due to the highest impulse velocity during the detonation of blast. Also, it is observed that the

stress in concrete was found to be increased when the mass of TNT increased from 6 to 8 kg,

whereas the trend is reverse when the mass of TNT increased from 8 to 12 kg. The von-Mises

stresses in steel reinforcement against blast load of varying mass of TNT is shown in Fig. 9(a-v)-

(c-v). The von-Mises stress at the steel reinforced bar was found to be 494, 525 and 555 MPa for

6, 8 and 12 kg mass TNT respectively. It is observed that the stress was found to increase with

increase in mass of TNT. Therefore, it is concluded that the steel reinforcement was found

observing the stresses efficiently then the concrete when the mass of TNT is significantly higher.

Therefore, it is concluded that the maximum stress in the concrete was found to be in the range of

15 to 20 N/mm2 and is almost constant against 6, 8 and 12 kg charge weight.

5.2 Effect of varying standoff distance

The simulations were carried out against varying standoff distance at constant mass of TNT,

i.e. 8 kg. The response of reinforced concrete slab was studied against varying standoff distance

and the standoff distance considered as 1.5, 2.0, 5.0 and 8 m. The behaviour of reinforced

concrete slab in terms of deflection, impulse velocity, Mises stresses in concrete and steel bar and

compression damage against varying standoff distance is shown in Figs. 11 and 12.

The displacement of slab against blast load of by 8 kg mass TNT originated at 1.5, 2, 5 and 8 m

from the surface is shown in Fig. 11(a-i)-(d-i). The maximum deflection was found to be 185,

87.9, 6.4 and 0.33 mm against 1.5, 2.0, 5.0 and 8 m standoff distance respectively. The maximum

deflection on slab was about 185 mm against 1.5 m distance and it is found to be more vulnerable.

The deflection of slab against 1.5 m standoff distance was found decreased to 47, 3.4 and 0.5% as

compared to the deflection of slab by 2, 5 and 8 m respectively. It is observed that given slab

doesn’t experience damage against 5 and 8 m standoff distance. It is also clearly seen that the

deflection reaches its peak value within 0.02 seconds i.e., from the time of detonation, see Fig.

12(a).

The impulse velocity due to blast at varying standoff distance has been shown in Fig. 11(a-ii)-

(d-ii). The maximum impulse velocity was found to be 13, 9.7, 2.83 and 1.04 m/s against 1.5, 2.0,

5.0 and 8 m standoff distance respectively. It is observed that the impulsive velocity was found to

decrease with increase of standoff distance. The reason may be due to the fact that the intensity of

impulse wave generated by blast tend to be weaker as standoff distance increases. The impulse

velocity against 1.5 m standoff distance was found decreased to 75, 22 and 8% as compared to 2, 5

and 8 m distance from the surface, respectively. As it was clearly seen that velocity reaches its

maximum within 0.02 seconds after which it is drops to almost zero, see Fig. 12(b). It is also

observed that the maximum velocity reaches the slab at 0.004, 0.005, 0.008 and 0.02 seconds by

1.5, 2, 5 and 8 m standoff distance, respectively.

The compression damage of slab against blast load of 8 kg mass of TNT at varying standoff

distance is shown in Fig. 11(a-iii)-(d-iii). The maximum compression damage was observed 0.336

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Fig. 11 (i) Deflection of slab (ii) impulse velocity (iii) compression damage and Mises stresses in (iv)

concrete and (v) steel at (a) 1.5 (b) 2 (c) 5 and (d) 8 m standoff distance

against 1.5, 2 and 5 m standoff distance, however the damage was found to be insignificant i.e.,

0.327, against 8 m distance. Also it was observed that the damage intensity was found decreasing

with increase of standoff distance. Therefore, it is observed that the compression damage index in

slab was found to be vulnerable against 1.5, 2 and 5 m standoff distance whereas the slab was safe

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(a) (b)

Fig. 12 Response in terms of (a) deflection and (b) impulse velocity function of time at varying standoff

distance

(a) (b)

Fig. 13 Response of slab in terms of (a) deflection and (b) impulse velocity against varying mass of TNT

function of varying standoff distance

against 8 m standoff distance. Therefore, it is concluded that the slab was found to be more

vulnerable upto the standoff distance of 5 m and thereafter slab found safe at given mass of TNT 8

kg.

The von-Mises stresses in concrete against blast load of 8 kg mass of TNT at varying standoff

distance is shown in Fig. 11(a-iv)-(d-iv). At 0.004 second time step, the maximum von-Mises

stress at the concrete was found to be 39.8, 36.9, 33.4 and 25.2 MPa for 1.5, 2, 5 and 8 m standoff

distance respectively. However, it is observed that the stress in concrete was found to be almost in

the range of 21-15 MPa after 0.004 second time step. The slab experienced highest stress at 0.004

second for 1.5 and 2 m standoff distance whereas the same was found at 0.016 second for 5 and 8

m distance. Also, it is observed that the stress in concrete was found to be decreased when the

standoff distance increase from 1.5 to 8 m. The von-Mises stresses in steel reinforcement against

blast load at varying standoff distance is shown in Fig. 11(a-v)-(d-v). The von-Mises stress at the

steel reinforced bar was found to be 525, 392, 205 and 82 MPa for 1.5, 2, 5 and 8 m standoff

distance respectively. It is observed that the stress was found to decrease significantly with

increase in standoff distance. Therefore, it is concluded that the concrete was found observing the

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stresses efficiently then the steel when the standoff distance is significantly higher.

5.3 Effect of varying standoff distance and mass of TNT

The influence of varying mass of TNT and varying standoff distance has been studied in the

previous Section 5.1 and 5.2 respectively. In the present section, the effect of combination of

varying standoff distance as well as varying mass of TNT has been discussed. The simulations

were carried out against varying standoff distance i.e., 1.5, 2, 5 and 8 m at varying mass of TNT,

i.e., 6, 8 and 12 kg. The behaviour of reinforced concrete slab in terms of deflection and impulse

velocity is shown in Fig. 13(a)-13(b).

It was observed from the Fig. 13(a) that the standoff distance increases the maximum deflection

in slab was found decreases significantly. At 1.5 m standoff distance, the maximum deflection was

found to be 322, 185 and 118 mm against 12, 8 and 6 kg mass of TNT respectively. At 2 m

standoff distance, the maximum deflection was found to be 174, 94, and 56 mm against 12, 8 and

6 kg mass of standoff distance respectively. At 5 and 8 m standoff distance, the deflection in slab

was found to be insignificant, even though the mass of TNT is very high. This is clearly seen from

the Fig. 13(a) that maximum deflection found almost zero against all given charge weight. This is

due to the fact that the intensity of impulse wave tend to be weaker as standoff distance increases.

Therefore, it is concluded that this phenomenon may be utilised in designing of important

structures like nuclear containment, airport building, security station, ministry and hospital

building which are prone to terrorist attacks by keeping the important structure away from the

boundary up to the distance at which blast effect is minimum.

It was observed from the Fig. 13(b) that the standoff distance increases the maximum impulse

velocity generated in slab was found decreases significantly. At 1.5 m standoff distance, the

maximum velocity was found to be 18.6, 13.2 and 10.9 m/s against 12, 8 and 6 kg mass of TNT

respectively. At 2 m standoff distance, the maximum impulse velocity was found to be 13, 9.7 and

8.1 m/s against 12, 8 and 6 kg mass of standoff distance respectively. At 5 and 8 m standoff

distance, the velocity of impulse was found to be insignificant, i.e. 3 m/s irrespective of charge

weight. It is observed that when the standoff distance increases and weight of TNT decreases, the

maximum impulse velocity found decreases, this implies that velocity is inversely proportional to

standoff distance and directly proportional to charge weight.

5.4 Effect of varying boundary condition

Due to non-uniformity in buildings supports and structures one could find the different end

boundary conditions. The support conditions of reinforced concrete slab was considered based on

the provisions made by Indian standard practices, IS 456:2000. The behaviour of reinforced

concrete slab in terms of deflection, impulse velocity and Mises stresses in concrete element

against varying standoff distance is shown in Figs. 14-18.

The deflection of slab having different boundary conditions function of time is shown in Fig.

14. It was observed that maximum deflection reaches its peak value within the time step 0.02

seconds for all the boundary conditions except slab with three adjacent edge discontinuous. The

deflection of slab having three adjacent edge discontinuous found increased upto time step 0.06

second, thereafter the deflection of slab is constant. The maximum deflection in slab of different

boundary conditions such as all edges continuous, two long adjacent edges discontinuous, two

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Fig. 14 Deflection of slab at different boundary conditions function of time

Fig. 15 Maximum deflection in slab having (a) all edges continuous (b) 2 long adjacent edges

discontinuous (c) 2 short edge discontinuous (d) 1 short edge discontinuous (e) 2 adjacent edges

discontinuous and (f) 3 adjacent edge discontinuous end conditions

Fig. 16 Impulse velocity in slab having different end conditions function of time

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Fig. 17 Maximum impulse velocity in slab having (a) all edges continuous (b) 2 long adjacent edges

discontinuous (c) 2 short edge discontinuous (d) 1 short edge discontinuous (e) 2 adjacent edges

discontinuous and (f) 3 adjacent edge discontinuous end conditions

Fig. 18 Mises stresses in slab having (a) all edges continuous (b) 2 long adjacent edges discontinuous (c)

2 short edge discontinuous (d) 1 short edge discontinuous (e) 2 adjacent edges discontinuous and (f) 3

adjacent edge discontinuous end conditions at 0.08 second

short edge discontinuous, one short edge discontinuous, two adjacent edges discontinuous and

three long edge discontinuous were shown in Fig. 15. The maximum deflection of slab subjected

to all edges continuous, two long adjacent edges discontinuous, two short edge discontinuous, one

short edge discontinuous, two adjacent edges discontinuous and three long edge discontinuous was

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observed 33.8, 185, 32, 33, 346 and 495 mm respectively. The maximum deflection was observed

when the slab subjected to three edges discontinuous and the minimum deflection when the slab

subjected to two short edges discontinuous. However the deflection of slab having boundary of all

edges continuous, two short edge discontinuous and one short edge discontinuous was found to be

almost same, 33 mm.

The velocity of impulse generated due to blast load and the response of slab having different

boundary conditions function of time is shown in Fig. 16. It was observed that maximum

deflection reaches its peak value within the time step 0.004 second for all the boundary conditions

except slab with two adjacent edge discontinuous. The maximum velocity generated against slab

having three adjacent edge discontinuous at 0.008 second time step. The maximum velocity which

are generated by slab of different boundary conditions such as all edges continuous, two long

adjacent edges discontinuous, two short edge discontinuous, one short edge discontinuous, two

adjacent edges discontinuous and three long edge discontinuous were shown in Fig. 17. The

maximum velocity generated by slab subjected to all edges continuous, two long adjacent edges

discontinuous, two short edge discontinuous, one short edge discontinuous, two adjacent edges

discontinuous and three long edge discontinuous was observed 7.87, 13.2, 6.99, 7.59, 17.08 and

17.53 m/s respectively. The maximum velocity was observed when the slab subjected to three

edges discontinuous and the minimum deflection when the slab subjected to two short edges

discontinuous. However the velocity generated by slab having boundary of all edges continuous,

two short edge discontinuous and one short edge discontinuous was found to be almost same, 7

m/s. It is observed that the boundary conditions of slabs affects the drop of impulse velocity after

peak. The drop of velocity was found to be steep for the slab having all edges continuous, two

short edge discontinuous and one short edge discontinuous and the time covered to zero velocity is

0.04 second. However, the drop of velocity is almost linear for the slab having two short edge

discontinuous, two adjacent edges discontinuous and three long edge discontinuous and the time

covered to zero velocity is 0.025, 0.045 and 0.068 respectively.

The von-Mises stresses in concrete against blast load by 8 kg mass TNT at 1.5 m standoff

distance and the response of slab having different boundary conditions at 0.08 second is shown in

Fig. 18. It is observed that maximum stress reaches its peak value within 0.008 second irrespective

of the boundary conditions. At 0.08 second, the maximum stress was observed when the slab

having three adjacent edges discontinuous and the minimum stress was observed when the slab is

discontinuous on two short edges discontinuous. The maximum stress developed by slab having all

edges continuous, two long adjacent edges discontinuous, two short edge discontinuous, one short

edge discontinuous, two adjacent edges discontinuous and three long edge discontinuous was

observed 19.7, 18.2, 11.0, 16.4, 18.4 and 21.9 MPa respectively. It is observed that behaviour of

slab in terms of von-Mises stress is almost similar for all edge conditions except two short edge

discontinuous. The stress developed in the slab having two short edge discontinuous was found

decreased by almost 30-50% as compared to other end conditions considered in the present study.

It is also observed that the deflection, impulse velocity and stress in slab having two short edge

discontinuous end conditions were 32 mm, 6.99 m/s and 11.03 MPa respectively and it seems to

be the best boundary conditions among the chosen configurations. Therefore, it is concluded that

the slab with two short edge discontinuous may be utilised in designing of important structures.

5.5 Effect of varying the type of blast

The influence of surface blast on reinforced concrete slab has been studied in the previous

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(a) (b)

Fig. 19 Deflection of slab due to surface and air blast with (a) function of time and (b) function of

standoff distance

Fig. 20 Deflection of slab due to air blast against (a) 1.5 (b) 2 (c) 5 and (d) 8 m standoff distance

(a) (b)

Fig. 21 Impulse velocity at concrete element due to surface and air blast with (a) function of time and (b)

function of standoff distance

Section 5.1-5.4. In the present section, the response of reinforced concrete slab against air blast has

been studied and compared with the surface blast load by 1.5 kg mass of TNT at varying standoff

distance. The behaviour of reinforced concrete slab in terms of deflection and impulse velocity,

von-Mises stresses in concrete is shown in Figs. 19-23.

The deflection of slab function of time against air and surface blast by 8 kg mass TNT at 1.5 m

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Fig. 22 Impulse velocity at concrete element due to air blast against (a) 1.5 (b) 2 (c) 5 and (d) 8 m

standoff distance

Fig. 23 Mises stresses in concrete against (a) 1.5 (b) 2 (c) 5 and (d) 8 m standoff distance at 0.08 seconds

standoff distance is shown in Fig. 19(a). The deflection of slab was found to be 185 and 68 mm by

surface blast and air blast respectively. For the given charge weight and standoff distance the

deflection due to air blast decreases by 63% as compared to the surface blast. It was clearly seen

from the deformed shape of slab that bending is more in surface blast due to which more stresses

are developed. This is due to the fact that in surface blast epicentre is located on the surface of the

structure under consideration while in the air blast epicentre is located in the air. It is clearly seen

that the deflection reaches its peak value in less than 0.02 second. This implies that the peak

attainment is same whether the blast is on surface or in the air.

The deflection of slab function of standoff distance by air blast and surface blast by 8 kg mass

TNT is shown in Fig. 19(b). At surface blast, the maximum deflection was found to be 185, 87.9,

6.4 and 0.33 mm against 1.5, 2.0, 5.0 and 8 m standoff distance respectively. At air blast, the

maximum deflection was found to be 75.2, 35.5, 4.1 and 0.33 mm against 1.5, 2.0, 5.0 and 8 m

standoff distance respectively, see Fig. 20. It is observed that the deflection decreased by 53%,

88%, 92% when standoff distance increases from 1.5 to 2m, 2m to 5m and 5 to 8m respectively. It

is clearly seen from the Fig. 19(b) that as the standoff increases beyond 5 m, the deflection of slab

for both surface blast as well as air blast converges and is almost equal to zero. This implies that

for greater standoff distance surface blast and air blast phenomenon are quiet similar. It is

concluded that surface blast produce more damage to the structure as compared to air blast for the

same standoff distance but as the standoff distance increases the intensity of damage caused by

both the blast are similar.

The impulse velocity developed by slab against air and surface blast by 8 kg mass TNT at 1.5

m standoff distance is shown in Fig. 21(a). The velocity of impulse was found to be 13.2 and 8.59

m/s by surface blast and air blast respectively. It was observed that velocity wave generated due to

impulse is maximum for surface blast. It is clearly seen that the velocity reaches its peak value in

less than 0.02 second. For the given charge weight and standoff distance the impulse velocity due

335


to air blast decreases by 35% as compared to the surface blast. This is due to the fact that during

air blast epicentre is located just at the point where blast is occurring whereas in case of air blast,

the epicentre is away from the surface.

The velocity function of standoff distance by air blast and surface blast by 8 kg mass TNT is

shown in Fig. 21(b). Due to surface blast, the maximum impulse velocity was found to be 13, 9.7,

2.83 and 1.04 m/s against 1.5, 2.0, 5.0 and 8 m standoff distance respectively. Due to air blast, the

maximum impulse velocity was found to be 9.24, 7.52, 1.98 and 0. 8 m/s against 1.5, 2.0, 5.0 and

8 m standoff distance respectively, see Fig. 22. It is observed that the velocity decreases by 19%,

74%, 60% when standoff distance increases from 1.5 to 2m, 2m to 5m and 5 to 8m respectively. It

is clearly seen from the Fig. 21(b) that as the standoff increases beyond 5 m, the impulse velocity

in slab for both surface and air blast is almost equal to zero. This also implies that for greater

standoff distance surface and air blast phenomenon are quiet similar. Therefore, it is concluded

that surface blast produce more damage to the structure as compared to air blast for the same

standoff distance however as the standoff distance increases the intensity of damage caused by

both the blast are similar. The variation of stress in concrete by air and surface blast for 8kg TNT

at 1.5 m standoff distance and the response of slab at 0.08 second by varying standoff distance is

shown in Fig. 23. The stress has been reaches its peak value in less than 0.008 seconds.

6. Conclusions

The present study addresses the finite element investigation on the behavior of reinforced

concrete slab against blast load. The numerical simulations were carried out using

ABAQUS/Explicit finite element model to predict the response of slab and results are compared

with the experimental available in literature. The simulations were carried out against varying

standoff distance, mass of TNT, boundary conditions and type of blast. The damage mechanism of

reinforced concrete slab was studied in terms of deflection, impulse velocity, von-Mises stresses

and compression damage of concrete and the following conclusions have been drawn.

• The maximum deflection of slab obtained from simulation was 185 mm which is very close to

the experimental results of 190 mm. The actual and predicted deformation of the slab as a result of

failure has been compared and almost exact pattern of deformation has been predicted through

numerical simulations.

• It is observed that the deflection in the slab was found to be increased by 156% when the

mass of TNT increased from 6 to 12 kg. It is concluded that for every increase of 33.33% weight

of TNT, the deflection increases by 52%. The velocity of impulse wave was found to be decreased

from 17 m/s to 11 m/s when charge weight reduced by 6kg. The maximum stress in the concrete

was found to be in the range of 15 to 20 N/mm2 and is almost constant for 6, 8 and 12 kg charge

weight.

• It was observed that the deflection in the slab at a standoff distance of 2 m, 5 m, 8 m is

decreased by 53%, 88% and 92% as compared to standoff distance of 1.5 m respectively. It was

concluded from the study that the velocity of impulse wave reduces drastically after 2 m standoff

distance.

• It is also observed that the deflection, impulse velocity and stress in slab having two short

edge discontinuous end conditions were 32 mm, 6.99 m/s and 11.03 MPa respectively and it seems

to be the best boundary conditions among the chosen configurations. The stress developed in the

slab having two short edge discontinuous was found to decrease almost 30-50% as compared to

336


other end conditions considered in the present study. Therefore, it is concluded that the slab with

two short edge discontinuous may be utilised in designing of important structures.

• The deflection in slab due to air blast decreases by 63% as compared to surface blast. The

impulse velocity due to air blast decreases by 35% as compared to the surface blast. This is due to

the fact that during air blast epicentre is located just at the point where blast is occurring whereas

in case of air blast, the epicentre is away from the surface.

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